If the lines in a system of linear equations are parallel, what is the system called? Enter the number that corresponds to the correct option:
1 - consistent system of equations
2 - dependent system of equations
3 - inconsistent system of equations
4 - independent system of equations
(1 point)
3 - inconsistent system of equations
3 - inconsistent system of equations
If the lines in a system of linear equations are parallel, the system is called an inconsistent system of equations. To understand why, let's explain the concept of parallel lines in a system of linear equations.
Parallel lines have the same slope but different y-intercepts. In the context of a system of linear equations, if the lines are parallel, it means that the equations representing those lines have the same slope but different y-intercepts.
For example, let's say we have the following system of equations:
y = 2x + 3
y = 2x + 5
In this case, both equations have the same slope, which is 2. However, the y-intercepts are different (3 and 5). Therefore, the lines represented by these equations are parallel.
Now, back to the options given:
1 - A consistent system of equations refers to a system where the lines intersect at a single point. This is not the case when the lines are parallel, so this option is incorrect.
2 - A dependent system of equations refers to a system where the equations represent the same line. This is also not the case when the lines are parallel, so this option is incorrect.
3 - An inconsistent system of equations refers to a system where the lines are parallel and never intersect. This is the correct option that corresponds to a system of parallel lines, as explained above.
4 - An independent system of equations refers to a system where each equation represents a different line, regardless of whether the lines are intersecting or parallel. Although this can apply to some cases of parallel lines, it does not specifically describe a system of parallel lines, so this option is not the best choice.
Therefore, the correct answer is option 3 - an inconsistent system of equations.